Joint Center for Housing Studies Harvard University Multiple-Home Ownership and the Income Elasticity of Housing Demand Eric S. Belsky, Zhu Xiao Di, and Dan McCue October 2006 W06-5 The authors would like to thank Greg Ingram, Michael Carliner, and Yu-Hung Hong for their review and comments. © by Eric S. Belsky, Zhu Xiao Di, and Dan McCue. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice is given to the source. Any opinions expressed are those of the authors and not those of the Joint Center for Housing Studies of Harvard University or of any of the persons or organizations providing support to the Joint Center for Housing Studies. © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice is given to the source. Introduction Traditional models of the income elasticity of demand do not account for the possibility that households may own two or more homes (Hansen et al. 1998). Although estimates of the number of second homes and the share of households who own them vary, it is possible to use existing surveys to narrowly define second homeowners to exclude those who may own additional properties purely or mostly for investment reasons and then model their housing choices (Carliner, 2002; U.S. Department of Housing and Urban Development, 2004). This topic is of interest because it stands to reason that households that divide their consumption of housing services among two or more properties may make different choices about their primary residences than households that own a single home. For example, those splitting their consumption among multiple homes may allocate less, all else equal, to their primary home and make decisions about the locations of their primary and second homes that have implications for urban form and the operation of land and housing markets. This paper examines the determinants of the ownership of multiple homes and the influence of multiple-homeownership on the income elasticity of housing demand. It explores the impact of owning multiple homes on the income elasticity of demand for just primary residences, as well as total housing consumption. To the extent feasible in the datasets used for this analysis, homes owned for purely investment purposes are excluded from the analysis because such investments are little different from investments in other non-housing assets. Homes that are not used by their owners at least in part for seasonal or occasional use do not produce a flow of housing services that they consume. If the intention is not to use them, there is little reason to expect ownership of such homes to affect the income elasticity of demand for primary residences. Of course owning a home always has an investment element to it because dollars invested in the home have opportunity costs and homes are typically leveraged investments. But the twin consumption and investment motives for homeownership are well established and have not prevented household level estimation of the income elasticity of housing demand. Both the American Housing Survey (AHS) and the Survey of Consumer Finances (SCF) are used to model second home demand but only the AHS is used to model the income elasticity of demand. A logistic regression is used to analyze the determinants of the demand for multiple-homeownership while log linear models are used to estimate the income elasticity © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. 1 of demand. We model the impact of the log of estimated permanent income on the log of value of primary homes for single and multiple home owners separately, after controlling for demographic characteristics, and with or without a dummy variable for having investment savings of $20,000 or more. The regression is then repeated to estimate the impact on the log value for the total of all homes owned by households with more than one home. These models test for possible differences in the income elasticity of demand for primary residences subject to the possibility of owning a second home for consumption purposes. The paper begins with a literature review on the extent and determinants of second home demand. With few empirical investigations of second homeownership to review, this part of the review is brief. The literature on estimating the income elasticity of housing demand is far richer. But much of it focuses on the proper way to measure income for the purposes of estimating the elasticity of demand, as well as other appropriate controls. Our interest is in the impact of second homes. Hence, we also indicate how allowing for multiple ownership might influence elasticities and advance hypotheses about the likely influences on the choice to own a second home. This section is followed by a discussion of data and methods, model findings, and conclusions. Literature Review Despite the growing market for second homes, there are very few studies of the determinants of demand for second homes or the propensity of persons to own second homes. While there are numerous studies on the income elasticity of demand for housing, our review found no studies that examined the impact of second homes on the income elasticity of demand either for primary residences or for all residences owned at least in part for consumption purposes. Propensities to Own Second Homes Previous studies of the propensity to own second homes have not used formal probability models to estimate the independent influence of different variables on the odds of owning a second home. Using US government data, Di, McArdle & Masnick (2001) explored the characteristics of the owners of second homes, as well as locations, definitions and measurements of second homes. The paper found that that second homes are owned primarily 2 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. by white, middle aged homeowners with high incomes, and that 40 percent of second homes are mobile homes, but it did not look at wealth of second homeowners. Looking at wealth, Gutierrez (1999) searched to find any evidence of a wealth effect on the demand for new second homes, but concluded that the data were too unreliable to draw definitive conclusions about whether the wealth building and economic prosperity of the late 1990s were associated with any increases in second home development in areas with large second home shares. Kochera (1997) reported rapid growth in recreational properties in the mid 1990’s, but also large numbers of unexplained “other” second homes not used for recreation or investment purposes. More recently, Carliner (2002) reviewed data on second homeownership from the decennial Census, AHS, HVS as well as surveys of homebuyer preferences from NAHB and NAR, and found that second homeownership is strongly associated with age of homeowners. He concluded that although the market still appears to be largely misunderstood, studies indicate that demand for second homes has been holding up and may accelerate somewhat with increases in income and wealth of homeowners and as more baby boomers enter age cohorts with traditionally higher second homeownership rates. In summary, research on the propensity to own a second homes have shown descriptively that age, race, and income are associated with second homeownership, while wealth, though not examined on a household level, has been generally assumed to play a role. No econometric research has been done to study determinants of second home ownership, nor, as discussed below, have studies been done to measure income elasticity of housing demand in the context of with and without considering second homes. Estimating Demand Equations There is a very rich body of research on the income elasticity of housing demand. Demand for housing is an embodiment of a consumer’s decision as to how much housing to consume. Standard theoretical models posit that demand for housing is a function of household income, the price of housing services, and the price of all other goods and services. The standard theoretical equation for the housing equation is a log-linear model: (1) log xi = β0 + β1log y + β2log pH + β3log p0 + u © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. 3 In this equation, xi is the annual real expenditure on housing services, y is income, pH is the relative price of housing, p0 is an index of the price of all other goods, and u is a disturbance variable. Using a log form, β1 is the true income elasticity and β2 is the true price elasticity of demand for housing. The Debate on Current vs. Permanent Income When it comes to housing demand models, household income is thought of two ways: current income, which is a highly transitory measurement for earnings in a single year, and permanent income, which is a long-term concept of what household income will be into the future. This concept is shown in equation (2), where Yi is current income, YiP is the permanent income component of current income, and YiT is the transitory income component of current income. (2) Yi = YiP + YiT As a durable good with high transaction costs, it is generally argued that decisions on housing consumption are based on a household’s permanent income (YiP ), and therefore the transitory income component of a household’s current income (YiT ) biases demand models that use current income (Yi ), and results in underestimates of demand elasticities. A review by Carliner (1973) found that demand models attempting to use measurements or proxies for permanent income have achieved significantly higher income elasticities than those using current income. Polinsky and Ellwood, 1979, revisited several studies and showed that, when substituted for each other within the same housing demand equation, permanent income elasticities average about 50 percent higher than those for current income. Polinsky and Ellwood used metropolitan housing sales price and income data to estimate their own measure of permanent income elasticity and found estimates ranging from 0.80 to 0.87 (Polinsky and Ellwood, 1979). Since then Goodman & Kawai (1982) have found permanent elasticities to be 100 percent greater than current income elasticities. Though it is generally agreed that permanent income is the appropriate measurement for household income within a demand model, there has been much debate over how to correctly estimate permanent income, and also how to treat current income in the process. Reid (1962) 4 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. approximated permanent income by using a restricted sample of households with stable incomes and using current incomes as a proxy for permanent incomes. Models by Muth (1965), Winger (1968), and DeLeeuw (1971) used city median incomes as proxies for permanent income, arguing that averaging incomes across metro areas eliminates transitory elements. Other studies, such as Carliner (1973) use a multiyear average of a household’s past four years of incomes to approximate permanent income. More recently, Goodman and Kawai (1982) define permanent income as the predicted value of a regression of current household income on the determinant variables of permanent income, with the residual being transitory income. The resulting equation derived from (2) is as follows: (3) Yi = φ0 + ΣjφjHj + ΣjφjNj + YiT where: (4) YiP = φ0 + ΣjφjHj + ΣjφjNj In (3) and (4), we see that ΣjφjHj is the sum of a vector of human capital components of permanent income and their respective coefficients (age, education, employment status), and ΣjφjNj is a sum of a vector of nonhuman capital components of permanent income. To determine permanent income, our model follows the methodology of Wachter and Megbolugbe (1992) in performing a Box-Cox transformation on the dependent variable of the permanent income regression with λ = 0.5, and then re-transforms the predicted value before including it in the demand model (see Appendix A for model results). Incorporating Demographic and Other Household Characteristics Housing demand models have grown to include a number of demographic variables in attempts to measure differing “tastes” for housing consumption among a cross section of households with differing characteristics (Goodman, 1990; Hansen, Formby, & Smith, 1998). There has been much disagreement as to the significance of demographic factors within demand models. In a review of several studies, Hansen et. al. (1998) suggests that exclusion of demographic variables likely to be correlated with permanent income, such as race, age, sex, © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. 5 and household size, will bias estimations of income elasticity, and that the direction of this bias is most likely upward. However, an earlier empirical study by Carliner (1973) finds income elasticity measurements from regressions using demographic terms are higher than those without. Another empirical study from Follain (1979) found income and price elasticities not sensitive to the presence of socio-demographic variables, and a third empirical study by Goodman (1990), found demographic interactions relatively insignificant for populations close to general population means but highly significant for populations away from means, such as those at very low or very high incomes. In light of this diverse array of findings, we felt it necessary to include demographic variables within our model, and that age, race, and family type were the most appropriate factors available within our dataset. Controlling for House-Price and Non-Housing Cost Indexes The standard demand model in equation (1) generates price and income elasticities of housing demand based on the utility of housing consumption relative to all other goods. Goodman & Kawai (1984), following examples from DeLeeuw (1971) and Polinsky and Ellwood (1979), estimate a demand model with demographic and housing characteristic variables but without a non-housing cost index, choosing instead to apply various fixed-effect coefficients within the Ordinary Linear Regression. Due to limited geographic data in the AHS dataset, our model uses this fixed-effect approach to control for relative differences in both house-price and non-housing costs based on regional location as well as metro / non-metro area location. Our fixed-effect estimated regression equation becomes: (5) log (hi ) = β0+ β1log yiP + ΣjφjZji + u Where hi is the value of housing consumption and Zji is a vector of our 12 geographic dummies to control for the relative price of housing and non-housing goods to the individual, as well as demographic and other housing characteristic dummy variables that potentially affect the demand for housing and control for fixed-effects on housing consumption within the model. 6 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. We use housing value as our measure of housing consumption (hi) in our equation. Researchers generally agree that housing consumption for homeowners is best approximated and more easily obtained as a standardized measurement of total housing value, rather than as annual expenditures on homeownership. The common method, used by Goodman and Kawai (1984), involves hedonic regression, whereby a household’s housing value is taken as a function of neighborhood and resident characteristics. The housing price index can be determined by the price of a standardized unit of housing according to the hedonic regression, and housing consumption can then be measured as housing value divided by the price of a standardized unit. Including geographic and socioeconomic characteristics within our fixedeffects model enables us to standardize housing value somewhat within the demand model; though using separate hedonic regressions would clearly be superior. Therefore, hi, in our model is approximated simply as the total value of housing. Controlling for Other Effects: Wealth and Elderly Status Wealth variables seem not to have been included in previous studies, although it may have an impact on the propensity of second home ownership and influence on income elasticity estimates. Also, although age has often been included in studies of income elasticity, its effect may not be linear and its interaction with income is very possible. The lack of these variables in previous studies encourages us to include them in our study. Measures and Magnitude of Second Home Demand This paper is not intended to reopen debates about the level of income elasticity of housing demand. Instead, it explores whether ownership of second homes influences the income elasticity of demand for primary residences or for the aggregate value of all homes that are owned, at least in part, for consumption. This is increasingly relevant given the apparent increase in second homeownership in recent years. Statistics on the extent of second homeownership and the number of second homes are often inconsistent. These inconsistencies mostly reflect differences in methods of data collection, especially in how questions about the purpose of vacant or additional owned properties are asked, but also as a result of differences in sample sizes, sampling procedures, and weighting procedures across surveys. © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. 7 The AHS, Housing Vacancy Survey (HVS), and decennial Census each contain estimates of the number of second homes based on interviewer efforts to determine the status of vacant units. The AHS and the HVS produce estimates of second homes (defined here as homes for seasonal or occasional use and homes occupied by those with a usual residence elsewhere) that are closer to each other than to the decennial Census, which consistently estimates a far smaller number of second homes. However, the AHS produced higher second home estimates than the HVS in the early to mid 1990s and then lower estimates thereafter (Carliner 2002). The HVS registered a strong 20 percent increase in the number of second homes from 1995 to 6.8 million in 2005 while the American Housing Survey reported a smaller but still substantial increase from 5.8 million in 1995 to 6.2 million in 2003. Many surveys ask households questions about whether they own additional properties and then ask them questions about these properties. These include the AHS, the SCF, the Survey of Income and Program Participation (SIPP), the Panel Study of Income Dynamics (PSID), and industry surveys such as one of new homebuyers conducted by the National Association of Home Builders (2000) and by the National Association of Realtors® (NAR) of homebuyers and homeowners. A recent NAR survey of 2005 homebuyers found that about 12 percent of all homes purchased were characterized by their owners as for vacation use and 28 percent for investment purposes. The intricacies of how all the other household surveys are conducted are well summarized by Carliner (2002) and the US Department of Housing and Urban Development (2004). Suffice it to say here that the SCF is the only dataset to ask questions about second homes on a regular (every three year) basis. Like the HVS, it shows growth in second home demand over the past decade (Chart 1). However, for all age groups except those now in their 60s, all of the growth was in households reporting timeshare fractional ownership in a second home. Overall, the SCF shows an increase of about 600,000 homes for “seasonal/vacation use” and in time shares of fully 1.8 million. Assuming that fractional ownership averages 2 week per year, then a 1.8 million increase in timeshare owners translates into only about 70,000 units. 8 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Share of households having timeshares 14% 12% 10% 8% 6% 4% 2% 0% 30s 40s 50s 60s 2004 1995 2004 1995 2004 1995 2004 1995 2004 Age Share of households having seasonal/vacation homes 1995 Share of Households Chart 1: Second Home Ownership Has Increased Across All Ages 70+ Source: SCF data While the figures shown here suggest that second homeownership rates among homeowners peak in their 50s and 60s at about 6-6½ percent, and rates of time shares peak at about 5 percent, these may be undercounts. The reason is that when SCF respondents are asked what type of property they own, they must choose from “seasonal/vacation home,” “time share ownership,” and a host of structure types including single-family house, condominium, residential, trailer/mobile home, farm/ranch, etc. It is likely that some of those who own homes for occasional use on weekends or for work do not consider them for seasonal or vacation use. Indeed, many of those responding with a structure type do not derive any rental income from their second home, suggesting that in some cases they are at least in part for consumption uses. With an even greater number of households headed by younger boomers growing into the 50-59 age group by 2015 than the number of households headed by leading edge boomers currently in that age, and each generation accumulating more household net wealth and higher median incomes than previous generation at similar age, demand for second homes are likely to continue to grow in the coming decade (Belsky and Prakken 2004). Hypotheses The literature and economic theory suggest the following hypotheses with respect to the likelihood of owning a second home and the impact of owning a second home on income elasticities for housing: © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. 9 A) The likelihood of owning a second home will be increasing with permanent income, current income, wealth, and age. Higher incomes and wealth allow consumers to allocate more of the household budget to housing consumption and investment. Lifecycle factors suggest that even after controlling for income and wealth, second homeownership might be higher for older aged households as they approach or reach retirement and look towards more leisure time. But the impact of the presence of children is more ambiguous because on the one hand it may increase the utility derived from a second home, but on the other may be a drain on the household budget. Geographic location of the primary residence might also have an influence, but again is ambiguous. With most owners having second homes within driving distance of their primary residences, living in a lower cost area could increase the likelihood of owning a second home because the costs of buying a second home are lower. On the other hand, these same areas tend to have lower price appreciation and therefore leave owners with less housing wealth to leverage up for second homeownership. B) The income elasticity of demand for primary residences will be lower for those with second homes than for those with just one home. There are several factors that lead to this expectation. First, households that have a preference for owning second homes divide their housing consumption among more than one property. Because they split their consumption between two homes, one would expect the income elasticity of demand for just their primary home to be lower than for owners of only one home. This holds true whether the initial decision on how much to spend on a primary residence was made with the intention of buying a second home or if instead, over the lifecycle, a homeowner decides to adjust their housing consumption upward by investing in a second home rather than trading-up to a higher valued home or improving their primary residence. Second, second home owners have higher average incomes and housing consumption levels relative to owners of just one home. Indeed, their average income is very close to that of owners in the upper income quartiles of a just a single residence. Therefore, second home owners may be closer to being fully housed. In this case, uses of an incremental dollar other than housing may maximize their overall utility. As a result, increases in income may not in turn result in as large a percentage change in 10 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. consumption in their primary (or secondary) homes. Lastly, owners of a single home with no desire for second homeownership may have more of an incentive to maximize the quality and consumption value of their sole home, while those with a propensity to own second homes may under-consume their primary house in favor of second home ownership. C) The income elasticity of demand with respect to all houses owned by second homeowners will be lower than the elasticity of just their primary property. With consumption split, spending on the primary home will take precedence over spending on the secondary home, and therefore lower elasticities of secondary home demand will drag down overall elasticities of demand which incorporate both primary and secondary home consumption. Given the same income distribution, the income elasticity of demand for the primary home (eP) relates to the elasticity of the second home (eS) as a ratio based on the way in which consumption of these two goods relate to each other, based on the formula 1 : (6) eS = eP (% Change S / % Change P) With this equation, if both primary and secondary consumption are treated equally, the two income elasticities are equal. But we posit that consumption of primary home is the first priority because that is where homeowners spend more of their time. Therefore an incremental dollar will contribute more to consumption of a primary home than a second home. Thus, eS is less than eP. So it follows that the elasticity of total housing consumption should be higher than the elasticity for the second home, but lower than for primary home consumption. This should be at least true for non-elderly but seniors may spend half or even more time in their second homes. 1 With income Y, the primary elasticity is : eP = (dP/P) / (dY/Y) and the second is eS = (dS/S) / (dY/Y); Solving for y in the former equation, we obtain Y = (eP*P*dY)/dP and substituting this into the latter equation, we have: eS = eP * (dS/S)/(dP/P), which can be re-written as: eS = eP * [(% Change S) / (% Change P)]. © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. 11 D) The income elasticity of demand with respect to all properties owned by those who have second homes for consumption purposes will be lower than that of single-home owners. This is because, similar to the reasoning in (B) above, second homeowners, being on average older with high levels of wealth and income and high levels of housing consumption already, are less likely to be under-housed than the generally lower income owners of a single home. Therefore, income increases are not matched by the same increases in housing consumption seen by the generally lower income owners of a single home only. This may be tested and seen through decreasing elasticities of demand among single-home owners as income levels increase. E) Models that do not include the value of second homes and do not control for second homeownership are likely to produce biased estimates of the income elasticity of housing demand. This is because the ownership of multiple homes is expected to influence the income elasticities of demand in the ways stipulated in (A)-(D) above. Data and Method We use the AHS and SCF to provide empirical evidence on determinants of secondhome ownership and AHS to explore income elasticity of housing demand when second homeownership is considered. The AHS is conducted by Census for HUD every two years at the national level, and only twice (in 1985 and 1995) did it have a supplemental survey on second homes. In these years, respondents were asked about other residential properties they owned in addition to their primary homes. For these properties, up to 6 such properties are surveyed. For each recorded property, it asks respondents about why they hold such a property and asks them to mark all the reasons that apply. In our paper, we only look at those properties that are marked for recreational use in order to narrow the field as much as possible to households that self-report homes that they view, at least in part, as providing them a flow of housing consumption services. The regular AHS survey contains detailed household information including current household income, age, race/ethnic background, the education level of household heads, and family type. Unfortunately, geographic detail in the dataset is lacking. While about 100 metropolitan areas are specified, in most cases the number of observations is far too few to 12 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. create a meaningful hedonic price index. Instead, to control for differences in the costs of housing and non-housing goods across areas, we rely on the interaction of the 4 census regions and 3 types of metropolitan status (cities, suburbs, or non-metro). This provides 12 variations—an admittedly crude control for housing price differences across the country. The AHS also has a dummy variable on whether the household has investment savings of $20,000 or more. This is a crude proxy for the level of non-housing wealth of a household. This could have an impact on the income elasticity of housing demand but the current literature overlooks potential wealth effects on income elasticity. Particularly for the propensity of second-home ownership, it may have some influence as a determinant. Exhibit 1 shows basic descriptive statistics on the variables from the AHS we use to model propensities and elasticities. Because AHS top-codes the value of primary homes at $375,000, we drop these roughly 3 percent of cases in all of our elasticity models to avoid using exactly the same value for all records with house values at the top code. Importantly, the second home value is not top-coded, so models of the total value of properties owned by people who own a home under $375,000 in 1995 are not right-censored on second-home value. We also exclude a couple of hundred cases (less than one percent of the entire sample) in our elasticity models involving owners of multiple homes where no information on the value of second homes was provided. The SCF is conducted by the Federal Reserve Bank every three years. The most recent survey is 2004 and was just released in March 2006. The survey was originally designed to measure all kinds of debt that people take on, and thus has very rich information on liabilities vs. assets and therefore the net wealth held by each household surveyed. Because of the imbalances in wealth holding and distribution, the SCF over samples wealthy households. Roughly half of its sample is a set of wealthy households and the other half are households distributed across a greater spectrum of household wealth. Because of that, we have to use a weighted sample in modeling work. One of the benefits of this sampling procedure is that it insures better accuracy at the level of aggregate household net wealth. Therefore, one of the advantages of using the SCF data to model the probability of owning a second home is that SCF data provide the most accurate and detailed wealth information of any household survey. With this data, we are able to obtain non-housing wealth as a variable that omits home equity, which is too closely © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. 13 correlated to our dependant variable of home value and would induce bias our model. This is more precise than the AHS dummy indicator of savings in excess of $20,000. The biggest limitation of the SCF data is that it has a small sample size of less than 5,000 households. Because of that, the released file for public use does not have any geographic variables. This prevents us from controlling for any house price variation across even regions or metropolitan status. It also prevents meaningful estimation of permanent income. For this reason, we only use SCF data to model the propensity of owning a second home. The SCF also has some intrinsic problems embedded in the questionnaire design. As noted above, the coding system is such that some households may have chosen structure type categories such as singlefamily or multi-family units even though the home they own is for their own seasonal or occasional use. Exhibit 2 displays some descriptive statistics of homeowners in the SCF data. Because we run models on weighted samples, both un-weighted and weighted statistics are displayed. The two different datasets have different estimates on the share of vacation home owners among all households. While 2004 SCF data indicate a 3.7 percent vacation homeownership rate, the 1995 AHS data show a 3.3 percent rate. That is not surprising when considering the growth of vacation homes during the decade and differences in how questions about the purpose of second properties are asked. In both data, we exclude timeshare units from our count of recreational second homes. With the compelling theoretical and empirical arguments for using permanent income rather than current income as the appropriate correlate to estimate income elasticity, in our preferred AHS models we use the Box-Cox square root transformation in a two-step method first estimating household permanent income as described in Appendix A and then plugging in predicted values into the propensity and income elasticity of demand regressions. We did not estimate permanent income in SCF data because it lacks any kind of geographic information control for regional wage differentials. Thus, in our models using AHS data we put in permanent income while in our propensity model using SCF data we put in both current household income and the education level of household heads, which is often a proxy indicator for permanent income. In our elasticity models, we run non-elderly (Table 4a) and elderly (Table 4b) samples separately, as we suspect they may have statistically significant differences in elasticity with 14 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. respect to permanent income, especially since our predicted values for permanent income are apt to have larger residual errors for older people because the correlation of current incomes and the right-hand side predictors is weaker for retirees. We also run models with (Tables 4a/4b) and without (Tables 4c/4d) the wealth variable to see how it affects other coefficients, especially income elasticities. In Model 1, we estimate the elasticity among those who own only a single home, using the value of primary home as the dependent variable. In Model 2, we estimate the elasticity of demand for just the primary residence among those who own more than one home, again using the value of primary home as the dependent variable. This is our principal test of the hypothesis that the income elasticity of demand for primary residences will be lower for second homeowners than others because they split their consumption among multiple properties. In Model 3, we estimate the income elasticity of demand using total value of all homes owned by owners with second homes as the dependent variable to test the hypothesis that it will be lower because a percentage point increase in income will bring about a smaller percentage point increase in a larger combined first and second home total value. In Model 4, we estimate the income elasticity of demand just for second homes among second homeowners to test the hypothesis that it will be lower than the primary home demand elasticities, indicating relatively low income elasticities for second home demand, preference for primary home consumption, and most importantly, the negative influence of second home ownership on demand elasticities for total housing consumption. In Model 5, we present a single model of housing value for all homeowners with a dummy variable indicating ownership of a second home. This is included to provide an unbiased estimate of the income elasticity of housing demand that incorporates the possibility of second home ownership. Lastly, we perform a secondary test of the hypothesis that, because they have higher average incomes than the general population of homeowners that own just one home, second home owners have lower elasticities of demand for primary residences. To accomplish this, we divide the owners of one home into income quartiles to see if the income elasticity of demand is in fact lower among owners with average incomes similar to the population of second home owners. It should be noted that our data do not include geographic controls for second home location. Therefore, since our models proxy housing consumption with house value, © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. 15 uncontrolled-for location-based differences in appreciation levels of second homes may bias measurements of income elasticities based on current second home values. Although most second homes are within driving distance of the first home and may have similar rates of appreciation, if a significant number of second homes bought at the same price point had significantly different appreciation rates, then the current value does not equally reflect total home consumption. In the end, we assume that second home location and appreciation rates have some effect on income elasticities and owners’ adjustments to housing consumption that lie beyond the scope of this paper. The functional form of our propensities models is logistic and the form of our elasticity models is log-linear. Hence the variables in propensities infer differences in the odds of owning a home conditional on each individual variable holding the others constant. The coefficients on income in the log-linear models can be interpreted as the elasticity of housing demand with respect to income and assumes constant elasticities across all values of the dependent variables. More formally, our logit model takes the following form: (7) P(Si ) = φ0 + φ1YiP + φ2MINORITYi + ΣψjAGEji + ΣτkFAMILYki + ΣωlGEOGRAPHYli + φ3ELDERINCOMEi + Ui Where P(Si ) is the probability of owning a second home, YiP is permanent income, MINORITY is a dummy variable indicating whether or not the household head is non-Hispanic white (1 if minority and 0 otherwise); AGEj is 4 dummy variables flagging 10-year age cohorts (35-44 years, 45-54 years, 55-64 years, and 65+ years old, with under 35 as the reference group); FAMILYk is 5 dummy variables flagging the type of family (married with children, single parents, other family type, single person, and other non-family type, with married without children as the reference group); GEOGRAPHYl is 11 dummy variables controlling for regional and metropolitan level fixed effects (Northeast suburb, Northeast non-metro, Midwest city, Midwest suburb, Midwest non-metro, South city, South suburb, South non-metro, West city, West suburb, West non-metro, with Northeast city as the reference group), and Ui is a disturbance variable. In our propensity model using AHS data we also include an interaction 16 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. variable ELDERINCOME containing the income of elderly assuming their income may have quite different impact on second home ownership. Our elasticity models take the following form: (8) log (hi ) = β0+ β1log yiP + β2SAVINGSOVER20K + β3MINORITYi + ΣτkFAMILYki + ΣωlGEOGRAPHYli + Ui Where hi is the value of the primary home or the total value of all homes; yiP is the predicted permanent income; wi is a dummy variable flagging household savings and investments of over $20k (1 if yes and 0 otherwise); MINORITY is a dummy variable indicating whether or not the household head is not non-Hispanic white; FAMILYk is 5 dummy variables flagging the type of family (married with children, single parents, other family type, single person, and other non-family type); GEOGRAPHYl is 11 dummy variables controlling for regional and metropolitan level fixed effects (Northeast suburb, Northeast non-metro, Midwest city, Midwest suburb, Midwest non-metro, South city, South suburb, South nonmetro, West city, West suburb, and West non-metro); and Ui is a disturbance variable. Findings from the Propensity Models Models run on both the AHS and SCF data find that age is the most predominant determinant for vacation homes. The AHS model finds that the odds of owning a vacation home are 3.7 times higher for 45-54 year olds than the odds for those under 35. For the age group between 55 and 64, the odds ratio is as high as 6.5. In our SCF model, the numbers are even more dramatic. Compared to the odds for household heads under 35, the odds of owning a vacation home are 11.2 times as large for those between 55 and 64 years old. Why this should be true even after controlling separately for income and especially wealth (which we can do with some precision in the SCF model) is unclear. Wealth is correlated with age so it is conceivable that the estimates on age are biased and picking up some of the wealth effect. It could also be that at later ages, mortgage payments of homeowners make up a smaller share of their overall budget, freeing them up to spend more on a second home. Nevertheless, it seems © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. 17 plain that lifecycle matters a great deal when it come to the likelihood of owning a second home. Both datasets suggest that minority households are less likely to own second homes, all else equal. Both income (current and permanent) and non-housing wealth are positively associated with second homes in both datasets. But in our propensity model using SCF data, though these two variables are statistically significant, they have little practical impact. With $10,000 more non-housing wealth, a household’s odds ratio of having a vacation home vs. not having one is only 1.001, and a $10,000 increase in household current income only raises the ratio to 1.005. Again, this is surprising and suggests that the correlation of age with wealth and income may be distorting the results. In the SCF data, education is positively associated with owning a second home. The estimated odds that a college educated household head would own a vacation home versus no vacation home are over 4 times more than that of a household head with less than high school education. In AHS data, there is statistically significant interaction between permanent income and elderly status, suggesting that the impact of permanent income on propensity is indeed different for elderly and non-elderly households. None of the geographic dummy variables in AHS is statistically helpful in predicting second homes. So second-home ownership is not favored or disfavored by homeowners in any particular location regarding their primary residence. Having investment savings of more than $20,000 in the AHS data or higher level of non-housing wealth in the SCF data is more likely to own a vacation home. Exhibit 3a and 3b show our propensity models in AHS and SCF data. The patterns observed in two different data sets collected 9 years apart seem amazingly consistent. Findings from the Elasticity Models We obtain log-linear estimates in our elasticity models. Both among the non-elderly and elderly households, our models show that vacation home owners have somewhat lower income elasticity of demand for primary housing (Model 2) compared to those not having vacation homes (Model 1). When adding the value of vacation homes to that of primary homes, the elasticity is further lower (Model 3) compared to those without second homes, having been dragged down by very low demand elasticities for second homes (Model 4). For comparison to 18 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. the above, our estimate of the normal income elasticity of demand for all housing consumption among all homeowners (Model 5) shows that there is a slight positive bias in models that fail to incorporate the lower fixed effects behind second homeownership. These results are in line with our expectations. In our models, income elasticity estimates among the non-elderly sample are higher than those found among the elderly sample, though in part this reflects larger sample sizes for the non-elderly. Taking out the dummy variable on investment savings of $20,000 or more does not change the elasticity pattern (see Exhibit 4c-4d in comparison to 4a-4b). Our additional test of income elasticities by income level for those not owning a vacation home (Exhibit 5) shows decreasing income elasticities of demand as income levels rise, 2 supporting our hypothesis that the generally higher income level of second homeowners partly explains their lower overall elasticities of total housing demand relative to those not owning a second home. However, the very low elasticity levels of second homeowners go beyond what would be expected based on incomes alone. This final test provides compelling evidence that the choice to adjust consumption by adding a second home rather than by increasing the value of the primary residence (through trading up to a higher valued home or making improvements to an existing home) must lower demand elasticities for primary homes among second homeowners even more. Exhibit 6 summarizes our income elasticity models. It is worth noting that statistical significance tests revealed that for the non-elderly sample, the difference in coefficients of income elasticity of housing demand between those having and not having vacation homes was significant at the 90 percent confidence level, both in models with and without the wealth variable. For the elderly sample in neither case is the difference in elasticities significant. Conclusion The propensity models reported here are perhaps the first efforts to model the determinants of second home ownership. We find that especially the age of the household head but also the minority status of the household head and household income (both current and 2 The bottom income quartile is an exception perhaps because they have a higher utility for basic necessities other than housing. © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. 19 permanent), as well as household non-housing wealth are good predictors of second-home ownership. Our income elasticity models produce results consistent with the hypothesis that those having second homes have somewhat lower income elasticity of housing demand, as their resources have to be divided among more than one home. Even when including second home value in measuring housing consumption, homeowners with second homes still have lower income elasticity. 20 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Exhibit 1: Descriptive Statistics (AHS Data) Sample Group: Variables Less than High School High School Some College College Plus Minority Status Under 35 35-44 45-54 55-64 65+ Married Couple without Kids Married Couple with Kids Single Parent Other family Household Single Person Household Other Non-Family Household New England City New England Suburb New England Non-metro Midwest City Midwest Suburb Midwest Non-metro South City South Suburb South Non-metro West City West Suburb West Non-metro Total Value of All Homes Value of Primary Home Current Household Income Having Investment Savings of More than 20K Having Recreational 2nd Homes All Homeowners Unweighted N Yes % No 5,140 17.5 24,244 9,146 31.1 20,238 7,333 25.0 22,051 7,765 26.4 21,619 4,767 16.2 24,617 4,059 13.8 25,325 6,768 23.0 22,616 6,189 21.1 23,195 4,494 15.3 24,890 7,874 26.8 21,510 10,759 36.6 18,625 8,212 27.9 21,172 1,537 5.2 27,847 2,415 8.2 26,969 5,550 18.9 23,834 911 3.1 28,473 2,961 10.1 26,423 1,617 5.5 27,767 1,990 6.8 27,394 4,057 13.8 25,327 2,464 8.4 26,920 2,069 7.0 27,315 3,520 12.0 25,864 3,729 12.7 25,655 1,819 6.2 27,565 2,735 9.3 26,649 1,151 3.9 28,233 1,256 4.3 28,128 1,256 972 4.3 3.3 % Mean SD 82.5 68.9 75.0 73.6 83.8 86.2 77.0 78.9 84.7 73.2 63.4 72.1 94.8 91.8 81.1 96.9 89.9 94.5 93.2 86.2 91.6 93.0 88.0 87.3 93.8 90.7 96.1 95.7 117,520 90,148 115,092 84,158 48,741 38,091 28,128 95.7 28,412 96.7 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. 21 Exhibit 2: Descriptive Statistics (SCF Data) Sample Group: All Homeowners Variables Unweighted N Yes % No Less than High 1,418 8.6 14,977 School Education High School Education 3,349 20.4 13,046 Some College 2,870 17.5 13,525 College Graduate and Higher 8,758 53.4 7,637 Minority Status 2,397 14.6 13,998 Age Under 35 1,401 8.5 14,994 Age 35-44 2,905 17.7 13,490 Age 45-54 4,250 25.9 12,145 Age 55-64 3,983 24.3 12,412 Age 65+ 3,856 23.5 12,539 Married Couples 11,755 71.7 4,640 Male-headed Households 2,265 13.8 14,130 Female-headed Households 2,375 14.5 14,020 Total Value of All Homes Value of Primary Home Current Household Income Household Nonhousing Wealth Have Vacation Home 2,323 14.2 14,072 22 % Mean SD Weighted N Yes No Mean 91.4 10,084,611 13.0 67,329,712 87.0 79.6 82.5 21,595,072 27.9 55,819,252 72.1 17,012,350 22.0 60,401,974 78.0 46.6 85.4 91.5 82.3 74.1 75.7 76.5 28.3 28,722,291 14,894,182 10,341,166 15,783,863 17,988,831 13,517,649 19,782,815 47,580,287 86.2 12,963,143 16.7 64,451,181 83.3 85.5 16,870,894 21.8 60,543,429 78.2 37.1 19.2 13.4 20.4 23.2 17.5 25.6 61.5 48,692,033 62,520,141 67,073,158 61,630,461 59,425,493 63,896,675 57,631,508 29,834,037 62.9 80.8 86.6 79.6 76.8 82.5 74.4 38.5 1,187,458 3,112,890 263,594 456,240 870,106 1,882,222 246,807 359,768 1,061,331 4,499,026 87,069 250,929 12,259,998 46,399,527 85.8 SD 462,304 2,885,714 3.7 74,528,610 96.3 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Exhibit 3a: Propensity Model for Vacation Home Ownership (AHS Data) Dependent variable: Owning a Recreational Home Sample group: All homeowners Variable Intercept Permanent Income (in $10,000s) Having Savings & Investments Over $20K Minority Age 35-44 Age 45-54 Age 55-64 Age 65+ (Elderly) Married with Children Single Parents Other Family type Single Person Other Non-family type New England Suburb New England Non-metro Midwest City Midwest Suburb Midwest Non-metro South City South Suburb South Non-metro West City West Suburb West Non-metro Permanent Income(in $10,000s)*Elderly Coefficients -5.7521 0.2671 0.3951 -0.3973 0.8688 1.3011 1.8718 1.0153 -0.1936 -0.3904 -0.8844 -0.0958 -0.3631 -0.1537 0.0987 -0.0982 -0.0414 -0.1117 -0.0297 -0.1107 -0.2279 -0.1410 -0.0602 -0.2206 0.2660 Odds ratio *** ** ** *** *** *** *** ~ ns *** ns ns ns ns ns ns ns ns ns ns ns ns ns *** 1.306 1.484 0.672 2.384 3.673 6.5 2.76 0.824 0.677 0.413 0.909 0.696 0.857 1.104 0.906 0.959 0.894 0.971 0.895 0.796 0.869 0.942 0.802 1.305 Note: ~ p <.10 * p <.05 ** p <.01 *** p <.001 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. 23 Exhibit 3b: Propensity Model for Vacation Home Ownership (SCF Data) Dependent variable: Owning a Vacation Home Sample group: All homeowners Variable Intercept Household Income (in $10,000s) Non Housing Wealth (in $10,000s) High School Education Some College College Graduate and Higher Minority Status Age 35-44 Age 45-54 Age 55-64 Age 65+ (Elderly) Male-headed Households Female-headed Households Household Income(in $10,000s)* Elderly Coefficients -6.0876 0.0050 0.0009 0.3881 1.1650 1.4906 -0.9540 1.3422 2.2785 2.4220 2.1596 -0.5896 -1.5790 0.0030 Odds ratio * *** ns ~ * * ~ ** ** ** ~ *** ns 1.005 1.001 1.474 3.206 4.44 0.385 3.827 9.762 11.268 8.667 0.555 0.206 1.003 Note: ~ p<.10 * p <.05 ** p <.01 *** p <.001 24 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Exhibit 4a: Elasticity Model using Predicted Permanent Income & Wealth Variables (Non-Elderly) Sample group: Non-Elderly Homeowners Dependent variable: Sample Sub-Group: Intercept Predicted permanent income (in $10,000s) Having Savings & Investments Over $20K Minority Age 35-44 Age 45-54 Age 55-64 Married with kids Single parents Other family type Single person Other non-family type New England Suburb New England Nonmetro Midwest City Midwest Suburb Model 1 Value of primary home Do not own a vacation home -1.6110 Model 2 Value of primary home Own a vacation home 0.9363 Model 3 Total value of all homes Own a vacation home 3.1226 Model 4 Value of vacation home(s) Own a vacation home 3.1082 Model 5 Value of all homes All non-elderly homeowners 1.1814 *** 0.9741 *** 0.8343 *** 0.7237 ** 1.5382 1.1750 0.0341 ns -0.2720 ~ -0.3273 * -0.3932 ns 0.0206 ns 0.0213 0.0147 0.0452 0.2843 0.0719 0.3478 0.0539 0.3302 -0.0337 ns ns ** *** *** *** * *** ns 0.1925 -0.1388 -0.1167 0.1052 0.1220 0.3153 -0.0223 0.2166 -0.0802 ~ ns ns ns ns ns ns ns ns 0.0784 -0.1127 -0.0914 0.0091 0.0567 0.2272 0.1098 0.3546 -0.0525 ns ns ns ns ns ns ns ** ns 0.0489 -0.1530 -0.1143 -0.1894 -0.0756 0.1944 0.3299 0.5761 0.1189 ns ns ns ns ns ns ns ** ns ns ns ** *** *** *** * *** ns 0.2006 0.1056 *** ** 0.1257 0.3636 ns ~ 0.0116 0.3665 ns ** 0.1789 0.7736 0.0218 0.0145 0.0442 0.2805 0.0724 0.3454 0.0551 0.3317 0.0331 ns 0.1945 ** 0.1099 -0.1737 *** 0.1363 ns -0.0355 ns 0.0347 ns *** 0.0029 ns 0.0122 ns -0.1514 ns -0.0911 ns © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. 0.1732 - *** *** ** ns 25 Exhibit 4a: Elasticity Model using Predicted Permanent Income & Wealth Variables (Non-Elderly) Sample group: Non-Elderly Homeowners Dependent variable: Sample Sub-Group: Midwest Non-metro South City South Suburb South Non-metro West City West Suburb West Non-metro Own a Vacation Home R-squared Model 1 Value of primary home Do not own a vacation home Model 2 Value of primary home Own a vacation home Model 3 Total value of all homes Own a vacation home Model 4 Value of vacation home(s) Own a vacation home -0.1586 *** -0.0776 ns -0.2995 * -0.3196 ns -0.0479 ns -0.0986 ns -0.2755 ns -0.1047 ns -0.0263 ns 0.0576 ns -0.1005 ns 0.0630 ns -0.2027 *** 0.0411 ns -0.1694 ns -0.1764 ns 0.3884 0.3738 0.1520 *** *** *** 0.3840 0.3752 -0.1161 * * ns 0.2318 0.4075 -0.2153 ns ** ns 0.1494 0.5040 -0.0615 ns ~ ns 0.2354 0.2301 0.2630 .1287 Model 5 Value of all homes All non-elderly homeowners 0.0023 0.1631 0.0532 0.0286 0.2032 0.3843 0.3740 0.1426 0.6946 *** ns ns *** *** *** *** *** 0.2509 Note: ~ p <.10 * p <.05 ** p <.01 *** p <.001 26 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Exhibit 4b: Elasticity Model using Predicted Permanent Income & Wealth Variables (Elderly) Sample Group: Elderly Homeowners Model 1 Model 2 Model 3 Dependent Variable: Value of primary home Value of primary home Total value of all homes Model 4 Value of vacation home(s) Sample Sub-group: Do not own a vacation home Own a vacation home Own a vacation home Own a vacation home Intercept Predicted permanent income (in $10,000s) Savings & Investments Over $20K Minority Married with kids Single parents Other family type Single person Other non-family type New England Suburb New England Nonmetro Midwest City Midwest Suburb 4.3833 0.6643 *** 6.2127 0.5208 ** 6.8609 0.5230 ** 5.8369 0.5408 0.0749 ** -0.3180 * -0.3630 * -0.0451 0.0458 -0.2238 ns ns ns -0.2572 1.3486 0.0000 ns * NA -0.1809 1.5085 0.0000 0.0317 0.2980 -0.0305 ns *** ns 0.3511 0.2246 -0.1464 ns ns ns 0.2538 0.0584 *** ns 0.1125 -0.1768 -0.1281 0.0023 ** ns -0.2419 -0.2337 Model 5 Value of all homes All elderly homeowners ~ 4.4123 0.6618 *** -0.5054 ~ 0.0680 ** ns * NA -0.2659 1.9337 0.0000 -0.0484 0.0798 -0.2267 ns ns ns 0.2368 0.4152 -0.1108 ns * ns -0.0058 0.8192 0.2406 ns ~ N A ns * ns 0.0326 0.2976 -0.0306 ns *** ns ns ns -0.1024 -0.1438 ns ns -0.5305 -0.1841 ns ns 0.2471 -0.1438 *** ns ns ns -0.4009 -0.4886 ns ~ -0.6424 -0.9928 ns ~ -0.1297 -0.0053 ** ns © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. 27 Exhibit 4b: Elasticity Model using Predicted Permanent Income & Wealth Variables (Elderly) Sample Group: Elderly Homeowners Dependent Variable: Sample Sub-group: Midwest Non-metro South City South Suburb South Non-metro West City West Suburb West Non-metro Own a Vacation Home R-squared Model 1 Model 2 Model 3 Value of primary home Value of primary home Total value of all homes Model 4 Value of vacation home(s) Do not own a vacation home -0.0938 ~ 0.02576 ns -0.08877 ~ -0.15649 ** 0.45768 *** 0.33943 *** 0.20072 *** Own a vacation home -0.4499 ns -0.11892 ns 0.04567 ns 0.03585 ns 0.2668 ns 0.29476 ns 0.19681 ns Own a vacation home -0.7384 * -0.28319 ns 0.04439 ns -0.39357 ns -0.01365 ns -0.01042 ns -0.07404 ns Own a vacation home -1.1928 * -0.58427 ns 0.01921 ns -1.79853 ** -0.42189 ns -0.68952 ns -0.68283 ns 0.2798 0.2650 0.2066 0.1799 Model 5 Value of all homes All elderly homeowners -0.1013 ** 0.024 ns -0.0835 ** -0.15873 *** 0.45 *** 0.33476 *** 0.19816 *** 0.67716 *** 0.1990 Note: ~ p <.10 * p <.05 ** p <.01 *** p <.001 28 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Exhibit 4c: Elasticity Model using Predicted Permanent Income, No Wealth Control Variable (same as Model 4a but without “Savings & Investments over $20K”) Sample group: Non-Elderly Homeowners Model 1 Model 2 Model 3 Dependent variable: Value of primary home Value of primary home Total value of all homes Sample Sub-Group: Do not own a vacation home Own a vacation home Own a vacation home Intercept Predicted permanent income (in $10,000s) Minority Age 35-44 Age 45-54 Age 55-64 Married with kids Single parents Other family type Single person Other non-family type New England Suburb New England Nonmetro Midwest City Midwest Suburb Midwest Non-metro South City South Suburb -1.6109 1.1814 *** 0.7233 0.9941 *** 3.0282 0.8438 0.0208 0.0148 0.0456 0.2858 0.0720 0.3481 0.0539 0.3312 -0.0330 0.2004 0.1057 ns ns ** *** *** *** * *** ns *** ** 0.1923 -0.1417 -0.1288 0.1039 0.1252 0.3067 -0.0068 0.2157 -0.0968 0.1221 0.3322 ~ ns ns ns ns ns ns ns ns ns ~ -0.1738 0.0028 -0.1584 -0.0478 -0.0263 *** ns *** ns ns 0.1166 0.0066 -0.0901 -0.1098 0.0509 ns ns ns ns ns Model 4 Value of vacation home(s) Own a vacation home *** 2.8045 0.7523 0.0766 -0.1231 -0.1017 0.0074 0.0572 0.2129 0.1261 0.3468 -0.0763 0.0094 0.3285 ns ns ns ns ns ns ns ** ns ns ~ -0.0582 -0.1737 -0.3158 -0.2915 -0.1092 ns ns ~ ~ ns © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Model 5 Value of all homes All non-elderly homeowners ** -1.5378 1.1749 *** 0.0485 -0.1574 -0.1317 -0.1912 -0.0711 0.1818 0.3523 0.5745 0.0948 0.1738 0.7283 ns ns ns ns ns ns ns ** ns ns * 0.0215 0.0146 0.0444 0.2814 0.0724 0.3456 0.0550 0.3323 -0.0327 0.1944 0.1100 ns ns ** *** *** *** * *** ns *** ** 0.0063 -0.0995 -0.3378 -0.1209 0.0534 ns ns ns ns ns -0.1732 -0.0023 -0.1630 -0.0531 -0.0286 *** ns *** ns ns 29 Exhibit 4c: Elasticity Model using Predicted Permanent Income, No Wealth Control Variable (same as Model 4a but without “Savings & Investments over $20K”) Sample group: Non-Elderly Homeowners Model 1 Model 2 Model 3 Dependent variable: Value of primary home Value of primary home Total value of all homes Sample Sub-Group: Do not own a vacation home Own a vacation home Own a vacation home South Non-metro West City West Suburb West Non-metro Own a Vacation Home R-squared -0.2026 0.3886 0.3739 0.1527 0.2354 *** *** *** *** 0.0377 0.3682 0.3671 -0.1769 0.2250 ns ~ * ns -0.1757 0.2135 0.3993 -0.2893 0.2508 ns ns * ns Model 4 Value of vacation home(s) Own a vacation home -0.1814 0.1266 0.4923 -0.1494 .1238 ns ns ~ ns Model 5 Value of all homes All non-elderly homeowners -0.2032 0.3845 0.3741 0.1431 0.6949 *** *** *** *** *** 0.2509 Note: ~ p <.10 * p <.05 ** p <.01 *** p <.001 30 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Exhibit 4d: Elasticity Model using Predicted Permanent Income, No Wealth Control Variable (same as Model 4b but without “Savings & Investments over $20K”) Sample Group: Elderly Homeowners Model 1 Model 2 Model 3 Dependent Variable: Value of primary home Value of primary home Total value of all homes Model 4 Value of vacation home(s) Sample Sub-group: Do not own a vacation home Own a vacation home Own a vacation home Own a vacation home Intercept Predicted permanent income (in $10,000s) Minority Married with kids Single parents Other family type Single person Other non-family type New England Suburb New England Nonmetro Midwest City Midwest Suburb Midwest Non-metro South City South Suburb 4.3661 0.6663 *** 5.8300 0.5519 ** 6.4240 0.5586 ** 5.2286 0.5904 -0.0490 0.0400 -0.2265 ns ns ns -0.1962 1.3571 0.0000 ns * NA -0.1112 1.5182 0.0000 ns * NA -0.1688 1.9472 0.0000 0.0299 0.3037 -0.0262 ns *** ns 0.3317 0.1535 -0.1344 ns ns ns 0.2146 0.3340 -0.0970 ns ~ ns 0.2577 0.0623 *** ns 0.1136 -0.1441 ns ns -0.1011 -0.1065 -0.1228 0.0066 -0.0852 0.02862 -0.08564 * ns ns ns ~ -0.2140 -0.1814 -0.3940 -0.05629 0.06143 ns ns ns ns ns -0.3691 -0.4290 -0.6746 -0.21169 0.06238 Model 5 Value of all homes ~ All elderly homeowners 4.3983 0.6635 *** -0.0521 0.0744 -0.2292 ~ ns ns -0.0367 0.7062 0.2597 ns ~ N A ns * ns 0.1597 0.3029 -0.0267 ns *** ns ns ns -0.5286 -0.1321 ns ns 0.2507 0.0606 *** ns ns ns * ns ns -0.5981 -0.9098 -1.1039 -0.48473 0.04425 ns ns ~ ns ns -0.1249 -0.0017 -0.0938 0.02645 -0.08075 * ns ~ ns ~ © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. 31 Exhibit 4d: Elasticity Model using Predicted Permanent Income, No Wealth Control Variable (same as Model 4b but without “Savings & Investments over $20K”) Sample Group: Elderly Homeowners Model 1 Model 2 Model 3 Dependent Variable: Value of primary home Value of primary home Total value of all homes Model 4 Value of vacation home(s) Sample Sub-group: Do not own a vacation home Own a vacation home Own a vacation home Own a vacation home South Non-metro West City West Suburb West Non-metro Own a Vacation Home R-squared -0.15423 0.46045 0.34438 0.20717 0.1791 ** *** *** *** 0.10301 0.29434 0.30352 0.25103 0.2583 ns ns ns ns -0.3169 0.01778 -0.000414 -0.01215 0.2373 ns ns ns ns -1.69179 -0.37813 -0.67559 -0.59667 0.1901 Model 5 Value of all homes ** ns ns ns All elderly homeowners -0.15685 0.45241 0.3393 0.2037 0.67769 ** *** *** *** *** 0.1984 Note: ~ p <.10 * p <.05 ** p <.01 *** p <.001 32 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Exhibit 5: Demand elasticities decline with income among higher-income non-elderly homeowners, except for low-income households who have strived a lot to achieve homeownership Do not own a second home Annual Permanent Income Household Income Quartile Level High Over $61,578 HighMid $49,840 - $61,578 LowMid $40,140 - $49,839 Low Less than $40,140 Overall Mean $50,934 Income Elasticity of Primary Housing Demand 1.00 1.28 1.66 0.92 1.18 Own a Second Home Annual Permanent Income Elasticity of Household Income Primary Housing Income Elasticity of Total Level Demand Housing Demand Overall $56,568 0.97 0.83 Mean © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. 33 Exhibit 6: Summary Table of Income Elasticity of Housing Demand Sample Group: Non-Elderly Homeowners Dependent variable Sample Sub-groups Value of primary home Value of primary home Value of all homes Do not own a vacation home Own a vacation home Own a vacation home Income Elasticity With Wealth Without Wealth Control Control Variable 1.18137 *** 1.18136 *** 0.97407 *** 0.99413 *** 0.83426 *** 0.84375 *** Sample Group: Elderly Homeowners Dependent variable Sample Sub-groups Value of primary home Value of primary home Value of all homes Do not own a vacation home Own a vacation home Own a vacation home Income Elasticity With Wealth Without Wealth Control Control Variable 0.66429 *** 0.66632 *** 0.52075 ** 0.55193 ** 0.52298 ** 0.55856 ** Note: ~ p <.10 * p <.05 ** p <.01 *** p <.001 34 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. References Belsky, Eric and Prakken, Joel. 2004. Housing Wealth Effects: Housing Impact on Wealth Accumulation, Wealth Distribution, and Consumer Spending. National Association of Realtors® National Center for Real Estate Research. Carliner, Geoffery. 1973. Income Elasticity of Housing Demand. The Review of Economics and Statistics. Carliner, Michael. 1990. Second Home. Housing Economics, July Issue. Carliner, Michael. 1998. Second Home Construction. Housing Economics, July Issue. Carliner, Michael. 2002. Second Homes: A Growing Market? Housing Economics, July Issue. DeLeeuw, F. 1971. The Demand for Housing. Review of Economics and Statistics, February Issue. Di, Zhu Xiao; McArdle, Nancy; Masnick, George S. 2001. Second Homes: What, How Many, Where and Who. Joint Center for Housing Studies, Harvard University. Working Paper series N01-2. Fallis, G. 1985. The Demand For Housing. Housing Economics. Toronto: Butterworths. Goodman, Allen C. and Kawai, Masahiro. 1982. Permanent Income, Hedonic Prices, and Housing Demand: New Evidence. Journal of Urban Economics. Vol 12. Goodman, Allen C. and Kawai, Masahiro. 1984. Replicative Evidence on the Demand for Owner-Occupied and Rental Housing. Southern Economic Journal. Goodman, Allen C. 1990. Demographics of Individual Housing Demand. Regional Science and Urban Economics. Vol 20. pp. 83-102. Gutierrez, Rose. 1999. Second Homes: Well Hidden. Housing Economics, October Issue. Hansen J.L.; Formby J.P.; Smith W.J. 1998. Estimating the Income Elasticity of Demand for Housing: A Comparison of Traditional and Lorenz-Concentration Curve Methodologies. Journal of Housing Economics. Kochera, Andrew. 1997. “Second” Homes Owners by Households. Housing Economics, November Issue. Kohlhase, Janet E. 1986. Labor Supply and Housing Demand for One-and Two-Earner Households. The Review of Economics and Statistics. © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. 35 Muth, R. F. 1965. The Stock Demand Elasticities for Non-Farm Housing. The Review. 47, November Issue. National Association of Home Builders. 2000. What 21st Century Home Buyers Want. Polinsky, A. Mitchell, and Ellwood, David T. 1979. An Empirical Reconciliation of Micro and Grouped Estimates of the Demand for Housing. The Review of Economics and Statistics. Reid, M. 1962. Housing and Income. Chicago: University of Chicago Press. United States Department of Housing and Urban Development, 2004. How Many Second Homes Are There? Housing Market Conditions. Wachter, Susan M. and Megbolugbe, Isaac F. 1992. Racial and Ethnic Disparities in Homeownership. Housing Policy Debate. 3(2) Winger, A. 1968. Housing and Income. Western Economic Journal. 6. June Issue 36 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Appendix Table 1: Permanent Income Regression (Box-Cox λ=0.5) Variable DF Coefficient Intercept High School Some College College Graduate or Higher Minority Age 35-44 Age 45-54 Age 55-64 Age 65+ Married with children Single parents Other family type Single Person Household Other non-family type New England Suburb New England Non-metro Midwest City Midwest Suburb Midwest Non-metro South City South Suburb South Non-metro West City West Suburb West Non-metro 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Root MSE Adjusted R. Square N Mean Square 1.109E8 3725311 1.11E7 4.126E7 F Value Pr > F 403.86801 35.38528 65.19025 127.61739 Type II Sum of Squares 1.109E8 3725311 1.11E7 4.126E7 6785.57 227.91 679.24 2524.14 <.0001 <.0001 <.0001 <.0001 -24.84862 24.90867 33.39170 -7.97708 -81.02657 -4.44193 -100.95346 -41.75909 -116.24828 -38.83794 21.33853 -18.22930 -8.13391 4.77603 -25.81154 -17.94502 -12.29114 -36.61865 5.97286 5.68575 -24.32725 2040145 1501197 2498400 109798 1.294E7 60606 1.148E7 3199519 4.584E7 1178943 379576 222799 49158 20730 523873 241412 134174 1198814 24587 26090 334514 2040145 1501197 2498400 109798 1.294E7 60606 1.148E7 3199519 4.584E7 1178943 379576 222799 49158 20730 523873 241412 134174 1198814 24587 26090 334514 124.81 91.84 152.85 6.72 791.76 3.71 702.51 195.74 2804.29 72.13 23.22 13.63 3.01 1.27 32.05 14.77 8.21 73.34 1.50 1.60 20.46 <.0001 <.0001 <.0001 0.0096 <.0001 0.0542 <.0001 <.0001 <.0001 <.0001 <.0001 0.0002 0.0829 0.2601 <.0001 <.0001 0.0042 <.0001 0.2200 0.2065 <.0001 127.85071 0.3523 27908 © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. 37 Appendix Table 2: 38 Variable Definitions for Permanent Income Regression Variable Definition High School Some College College Graduate or Higher Minority Age 35-44 Age 45-54 Age 55-64 Age 65+ Married with children Single parents Other family type Single Person Household Other non-family type New England Suburb New England Non-metro Midwest City Midwest Suburb Midwest Non-metro South City South Suburb South Non-metro West City West Suburb West Non-metro 1 if high school graduate, 0 otherwise 1 if some college education, 0 otherwise 1 if college graduate, 0 otherwise 1 if minority, 0 otherwise 1 if 35-44, 0 otherwise 1 if 45-54, 0 otherwise 1 if 55-64, 0 otherwise 1 if 65 or over, 0 otherwise 1 if married with kids, 0 otherwise 1 if single parents, 0 otherwise 1 if other family type, 0 otherwise 1 if single person household, 0 otherwise 1 if other non-family type household, 0 otherwise 1 if NE suburb, 0 otherwise 1 if NE non-metro, 0 otherwise 1 if Midwest city, 0 otherwise 1 if Midwest sub, 0 otherwise 1 if Midwest non-metro, 0 otherwise 1 if South city, 0 otherwise 1 if South sub, 0 otherwise 1 if South non-metro, 0 otherwise 1 if West city, 0 otherwise 1 if West sub, 0 otherwise 1 if West non-metro, 0 otherwise © 2006 President and Fellows of Harvard College. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source.